Finite Group Databasebeta

C2×#13124136 #16729359

order3328
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C210

Aliases

direct productC2×#13124136

Splittings

FittingC22×C13×#135 ⋊ C2
SylowC13 ⋊ C2×#3012

Subgroups

subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC22×C13×#135C2
socleC23×C13C22×D4
hypercenterC22×#135D13
hypocenterC13C2×#3012
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#135

5126 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

400 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1036008);